# The local converse theorem for ${\rm SO}(2n+1)$ and applications | Annals of Mathematics

Abstract In this paper we characterize irreducible generic representations of SO2n+1(k) (where k is a p-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic cuspidal automorphic representations of SO2n+1(

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### 数学年刊（Annals of Mathematics）

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